Question

which equation best represents the relationship between x and y in the graph?
a. $y = -\frac{3}{4}x + 3$
b. $y = -\frac{4}{3}x + 4$
c. $y = -\frac{3}{4}x + 4$
d. $y = -\frac{4}{3}x + 3$

Explanation:

Step1: Identify the y-intercept

The y-intercept (b) is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at (0, 4), so \( b = 4 \). This eliminates options A and D which have \( b = 3 \).

Step2: Calculate the slope (m)

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's use two points on the line, e.g., (0, 4) and (4, 1).
\( m=\frac{1 - 4}{4 - 0}=\frac{-3}{4}=-\frac{3}{4} \).

Step3: Form the equation

The slope-intercept form is \( y = mx + b \). With \( m = -\frac{3}{4} \) and \( b = 4 \), the equation is \( y = -\frac{3}{4}x + 4 \), which is option C.

Answer:

C. \( y = -\frac{3}{4}x + 4 \)